After ZF detection, the SIC as one of the key components of NOMA technique is applied to separate superimposed signals sequentially. To simplify the design of power allocation coefficient and better utilize NOMA scheme, the decoding order at receivers is determined according to the decreasing order of transmission distances, i.e., \(d_K \ge \cdots \ge d_2 \ge d_1\)[1]}, [2]}. In particular, cluster \(k\)  will detect the message of cluster \(i\)  prior to decoding its own message \({\bf x}_k\)  such that \(i > k\) , and then subtracting the signal \({\bf x}_{i}\)  from its observation successively. In the meantime, the signal \({\bf x}_{i}\)  intended for cluster \(i\)  (\( < k\) ) will be regarded as interference at cluster \(k\) . Therefore, for the \(k\) -th nearest cluster to the BS, the instantaneous received signal-to-interference-plus-noise ratio (SINR) to detect the signal \(x_{m,i}\)  that is extracted from data stream \(m\)  is given by
\({\gamma _{m,k \rightarrow i}}&= \frac{{P{\zeta _{m,i}}}}{{P\sum \limits _{l = 1}^{i - 1} {{\zeta _{m,l}}} + \frac{\sigma ^2}{\ell ({d_k})}{{\left[ {{{\left( {{{\bf {H}}_k}{\bf {V}}} \right)}^\dag }{{\left( {{{\left( {{{\bf {H}}_k}{\bf {V}}} \right)}^\dag }} \right)}^{\rm {H}}}} \right]}_{mm}}}} \\&=\frac{{{{\bar{\gamma }}}{\ell ({d_k})}{\zeta _{m,i}}}}{{{{\bar{\gamma }}}{\ell ({d_k})}\sum \limits _{l = 1}^{i - 1} {{\zeta _{m,l}}} + {{\left[ {{{\left( {{{\left( {{{\bf {H}}_k}{\bf {V}}} \right)}^{\rm {H}}}{{\bf {H}}_k}{\bf {V}}} \right)}^{ - 1}}} \right]}_{mm}}}},\) 
